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Imposing a steady ionic current through an electrolyte results in the formation of salt concentration gradients that compromise battery performance. The limiting current is usually defined as the current at which the salt concentration at the cathode approaches zero. Higher currents cannot be imposed on the cell as larger concentration gradients are unsustainable. We study the limiting current in electrolytes comprising a perfluorinated oligomer, C8-DMC, and lithium bis(fluorosulfonyl)imide salt in symmetric lithium cells. The time-dependence of the potential, which increases as salt concentration gradients develop, was also measured. Both steady-state and transient behaviors are modeled using Newman’s concentrated solution theory; transport and thermodynamic parameters needed to perform the calculations were measured independently. The limiting current is a nonmonotonic function of salt concentration in both theory and experiment. The model shows that at low salt concentrations (below 0.88 mol/kg solvent), the concentration at the cathode approaches zero at limiting current. In contrast, at high salt concentrations (above 0.88 mol/kg solvent), the concentration at the anode approaches the solubility limit (2.03 mol/kg solvent). The experimentally determined salt concentration at which the limiting current is maximized is in excellent agreement with theoretical predictions made without resorting to any adjustable parameters.

The synthesis and polymerization of fused‐ring 1,7‐didodecyl‐1,7‐dihydrothieno[3,2‐b:4,5‐b′]dipyrrole monomer are reported. The FeCl3‐mediated oxidative polymerization and Stille coupling polymerization of the thienodipyrrole monomer were employed to generate homopolymers and an alternating copolymer with thiophene. The synthesized polymers have molecular weights ranging from 1600 to 6500 g mol−1and display the absorption maxima at ≈355 nm.

A function ƒ defined on the subsets of a set Sis n-alternating if a certain n-alternation deficiency function δnƒhas no negative values. In the case of a geometric rank-function r, δ1r⩾0 and δ2r⩾0 because ris non-decreasing and semi-modular. The only geometry G(r,S) for which δnr0,n⩾3, is the Boolean Algebra on S. Specializing to the case n=3, for any given non-negative integer p, the geometries for which min δ3r=…pare characterized by an excluded subgeometry.

A weak cut of a Combinatorial Geometry G is a generalization of a modular cut, corresponding to the family of the new dependent sets in a weak map image of G. The use of weak cuts allows the construction of all weak images of G, an important result being that, to any family $ {\mathcal{M}}$G, is associated a unique weak cut $ {\mathcal{C}}$ $ {\mathcal{M}}$ $ {\mathcal{C}}$ The notion of weak cut is particularly useful in the study of erections. Given a geometry F and a weak image G, an F-erection of G is an erection of G which is a weak image of F. The main results are that the set of all F-erections of G is a lattice with the weak map order, and that the free F-erection can be constructed explicitly. Finally, a problem involving higher order erection is solved.

There is growing interest in fluorinated electrolytes due to their high-voltage stability. We use full electrochemical characterization based on concentrated solution theory to investigate the underpinnings of conductivity and transference number in tetraglyme/LiTFSI mixtures (H4) and a fluorinated analog, C8-DMC, mixed with LiFSI (F4). Conductivity is significantly lower in F4 than in H4, and F4 exhibits negative cation transference numbers, while that of H4 is positive at most salt concentrations. By relating Stefan-Maxwell diffusion coefficients, which quantify ion-solvent and cation-anion frictional interactions, to conductivity and transference number, we determine that at high salt concentrations, the origin of differences in transference number is differences in anion-solvent interactions. We also define new Nernst-Einstein-like equations relating conductivity to Stefan-Maxwell diffusion coefficients. In H4 at moderate to high salt concentrations, we find that all molecular interactions must be included. However, we demonstrate another regime, in which conductivity is controlled by cation-anion interactions. The applicability of this assumption is quantified by a pre-factor, which is similar to the "ionicity" pre-factor that is often included in the Nernst-Einstein equation. In F4, is unity at all salt concentrations, indicating that ionic conductivity is entirely controlled by the Stefan-Maxwell diffusion coefficient quantifying cation-anion frictional interactions.